TWO-DIMENSIONAL VERSAL $ G $-COVERS AND CREMONA EMBEDDINGS OF FINITE GROUPS

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概要

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• Let $ G $ be a finite group. A Galois cover $ \bar{ \omega } \colon X \rightarrow Y $ with Galois group $ G $ is called a versal $ G $-cover if any $ G $-cover is induced from $ \bat{ \omega } \colon X \rightaroow Y $. In this paper, we prove that, if the essential dimension of $ G $ is equal to $ 2 $, then there exists a versal $ G $-cover $ \bar{ \omega } \colon X \rightarrow Y $ such that (i) $ X $ is a smooth rational surface, (ii) $ G $ is a finite automorphism group of $ X $, (iii) the action of $ G $ on $ X $ is minimal, and (iv) $ Y = X/G $. We also give some examples of finite groups which have non-conjugate embeddings into the Cremona group $ Cr_2(\mathbb{C}) $.

• Faculty of Mathematics, Kyushu Universityの論文

著者

• Tokunaga Hiro-o

  Department Of Mathematics And Information Sciences Tokyo Metropolitan University

• Tokunaga Hiroo

  Department of Mathematics and Information Sciences Tokyo Metropolitan University

関連論文

• Non-Galois triple covering of P^2 branched along quintic curves and their cubic equations
• TWO-DIMENSIONAL VERSAL $ G $-COVERS AND CREMONA EMBEDDINGS OF FINITE GROUPS

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